Research

Links to author profiles

My author profile on ZbMath, Orcid and Scopus.

Preprints

  • Conference Proceedings in honor of Manfred Denker’s 80th birthday (with Suzanne Boyd, Herold Dehling, Martin Schmoll and Christian Wolf). Special Session on Ergodic Theory and Dynamical Systems at the AMS Spring Southeastern Sectional Meeting, Clemson University, Clemson, SC, March 8-9, 2025.
  • From Ergodic Theory and Probability to Fractal Geometry and Dynamics: Themes in the Work of Manfred Denker (with Suzanne Boyd, Herold Dehling, Martin Schmoll and Christian Wolf). Preprint in arxiv
  • Amenable graphs and the spectral radius of extensions of Markov maps (with Johannes Jaerisch and Elaine Rocha). Preprint in arxiv.
  • On Spaceability within Linear Dynamics (with Manuel Saavedra). Submitted, preprint in arxiv.

Publications

  • Quasi-rigid operators and hyper-recurrence (with M. Saavedra). Accepted for publication in Studia Matematica (2025), preprint in arxiv.
  • Spectral triples and Dixmier trace representations of Gibbs measures: theory and examples (with L. Cioletti, L. Y. Hataishi, A. O. Lopes). Nonlinearity 37 (2024). Published version at doi, preprint in arxiv.
  • Minimal distance between random orbits (with S. Gouezel and J. Rousseau). Probability Theory and Related Fields (2024). Published version at doi, preprint in hal – archives ouvertes.
  • The Martin boundary of an extension by a hyperbolic group (with S. Bispo). Israel Journal of Mathematics 255 (2023), 1-62. published version, doi, arxiv.
  • Quenched and annealed equilibrium states for random Ruelle expanding maps and applications (with P. Varandas and X. Zhang). Ergodic Theory & Dynam. Systems 43 (2023), pp. 3150-3192 doi, arxiv. Published online 9/2022.
  • Invariant probabilities for discrete time linear dynamical systems via thermodynamic formalism (with A. Lopes, A. Messaoudi and V. Vargas). Nonlinearity 34 (2021), 8359-8391. doi, arxiv.
  • Thermodynamic formalism for random non-uniformly expanding maps (with S. Suzuki and P. Varandas). Communications in Math. Physics. 385 (2021), 369-427. doi, arxiv.
  • On the law of the iterated logarithm for continued fractions with sequentially restricted partial quotients (with X. Zhang). Nonlinearity 34 (2021), 1389-1407. doi, arxiv.
  • Ruelle Operator for Continuous Potentials and DLR-Gibbs Measures (with L. Cioletti and A. O. Lopes). Disc. Cont. Dyn. Sys. 40 (2020), 4625-4652. doi, arxiv.
  • Thermodynamic formalism for topological Markov chains on Borel standard spaces (with L. Cioletti and E. Silva). Disc. Cont. Dyn. Sys. 39 (2019) 6277-6298. doi, arxiv.
  • Spectral properties of the Ruelle operator for product type potentials on countable alphabets (with A. Lopes, L. Cioletti and M. Denker). Journal of the LMS 95 (2017) 684-704. doi, arxiv.
  • On the Lyapunov spectrum of relative transfer operators (with M. Bessa). Stochastics & Dynamics 16 (2016) 1650024-1 to 1650024-25. doi, arxiv.
  • Contraction in the Wasserstein metric for some Markov chains, and applications to the dynamics of expanding maps (with A. Lopes and B. Kloeckner). Nonlinearity 28 (2015) 4117-4137. doi, arxiv
  • Coupling methods for random topological Markov chains. Ergodic Theory & Dynam. Systems 37 (2017) 971–994. doi, arxiv, published online 2015.
  • Corrigendum to: Thermodynamic formalism for random countable Markov shifts (with M. Denker and Yu. Kifer). Disc. Cont. Dyn. Sys. 35 (2015), 593 – 594. doi, preprint.
  • Corrigendum and addendum to: On random topological Markov chains with big images and preimages.Stochastics & Dynamics 14 (2014).doi, preprint.
  • An extension of Kesten’s criterion for amenability to topological Markov chains. Advances in Mathematics 235 (2013) 450-468. doi, arxiv.
  • On random topological Markov chains with big images and preimages. Stochastics & Dynamics 10 (2010), 77-95. doi, arxiv.
  • Thermodynamic formalism for random countable Markov shifts (with M. Denker and Yu. Kifer). Disc. Cont. Dyn. Sys. 22 (2008), 131-164. doi.
  • Conservativity for random Markov fibred systems (with M. Denker and Yu. Kifer). Ergodic Theory & Dynamical Systems 28 (2008), 67-85.doi.
  • Lyapunov spectra for KMS states on Cuntz-Krieger algebras (with M. Kesseböhmer and B. O. Stratmann). Mathematische Zeitschrift 256(4) (2007), 871-893. doi, arxiv.
  • A remark on densities of hyperbolic dimensions for conformal iterated function systems with applications to conformal dynamics and fractal number theory (with B. O. Stratmann). Indagationes Mathematicae 17 (2006), 311 – 317. doi.
  • Infinite ergodic theory for Kleinian groups (with B. O. Stratmann). Ergodic theory & dynamical systems 25 (2005), 1305 – 1323. doi, Mathematica Gottingensis 10, 2003 (ps.gz).
  • The return sequence of the Bowen-Series map for punctured surfaces. Fundamenta Mathematicae 182 (2004), 221 – 240. doi.
  • The Bowen-Series map for some free groups. Mathematica Gottingensis 5, 2002 (ps.gz). PhD-thesis.

Articles in Proceedings

  • On conformal measures and harmonic functions. In the Proceedings of “New Trends in Onedimensional Dynamics, celebrating the 70th birthday of Welington de Melo”, p. 275-304 (2019). Doi 10.1007/978-3-030-16833-9, arxiv.
  • Foreword (with Artur Lopes and Samuel Senti) of the Proceedings to the conference “Probability in Dynamics” in Rio de Janeiro 2014. Stochastics & Dynamics (2016).
  • On thermodynamic formalism for group extensions. Mini-Workshop: “Thermodynamic Formalism, Geometry and Stochastics”. Oberwolfach Reports 9 (2012), doi, extended abstract.
  • Semiconjugacies for skew products of interval maps (with M. Denker). RIMS Kokyuroku 1404 (2004). Preprint (Kyoto).

Proceedings

  • Editor (with Artur Lopes and Samuel Senti) of the Proceedings to the conference “Probability in Dynamics” in Rio de Janeiro 2014. Stochastics & Dynamics 16, Issue 2 and Issue 3 (2016).

PhD-Students

  • Elaine Rocha: Extensão do critério de Kesten sobre amenidade para extensões por grafos de aplicaçães Gibbs-Markov. Thesis defense: 9/2019.
  • Sara Ruth Pires Bispo: A fronteira de Martin de uma extensão por um grupo hiperbólico. Thesis defense: 11/2019.
  • Manuel Jesús Saavedra Jiménez: On recurrence of linear operators. Thesis defense: 9/2023.
  • Deniel Corrêa de Almeida: Medidas Invariantes e Ergodicidade em Skew Product de Diagramas de Bratteli. Thesis defense: 8/2025.